Imprecise set and fuzzy valued probability (Q555115)

From the introduction: ``Imprecise probability is a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilties.'' In this paper, the range of set-valued probability is the set of subsets of the unit interval, and the range of fuzzy-valued probability is the set of fuzzy sets of the unit interval. The method of restricted set arithmetics is used to treat the set- or fuzzy-valued probabilities in spite of that the sum of all individual probabilities is one. The author introduces the set- and the fuzzy-valued probability as functions derived, respectively, from a finite complete set- and a fuzzy-valued measure. The used model is suitable to define an expectation. In the definitions and theorems, there is no assumption about convexity so, this theory can be used to model and to analyze probabilistic systems where the values of probability are highly imprecise but discrete. An example of application in finance is given.